<!DOCTYPE html>
<html lang="en-US">
<!--********************************************-->
<!--*       Generated from PreTeXt source      *-->
<!--*                                          *-->
<!--*         https://pretextbook.org          *-->
<!--*                                          *-->
<!--********************************************-->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="robots" content="noindex, nofollow">
</head>
<body class="ignore-math">
<h3 class="heading"><span class="type">Paragraph</span></h3>
<p><dfn class="terminology">Solution:</dfn></p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\begin{aligned}
\frac{Q(x)}{P(x)}&amp;=\frac{x}{x^2-2x-3}=\frac{x}{(x-3)(x+1)}=\frac{1}{4}\left[\frac{3}{x-3}+\frac{1}{x+1}   \right].
%&amp;=\frac{1}{4} \left[ \frac{3}{1+x-4} +\frac{1}{5+x-4}\right].\\
%\textrm{Since}~ &amp;\frac{3}{1+x-4}=\frac{3}{1+t}=3 [1-t+t^2-t^3+\cdots],\quad |t|&lt;1,\\
%&amp;\qquad \qquad=3 [1-(x-4)+(x-4)^2-(x-4)^3+\cdots],\quad |x-4|&lt;1.
\end{aligned}
\end{equation*}
</div>
<span class="incontext"><a href="sec5_3.html#p-215" class="internal">in-context</a></span>
</body>
</html>
